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A theory for particle size segregation in shallow granular free-surface flows
No full textGranular materials composed of a mixture of grain sizes are notoriously prone to segregation during shaking or transport. In this paper, a binary mixture theory is used to formulate a model for kinetic sieving of large and small particles in thin, rapidly flowing avalanches, which occur in many industrial and geophysical free-surface flows. The model is based on a simple percolation idea, in which the small particles preferentially fall into underlying void space and lever large particles upwards. Exact steady-state solutions have been constructed for general steady uniform velocity fields, as well as time-dependent solutions for plug-flow, that exploit the decoupling of material columns in the avalanche. All the solutions indicate the development of concentration shocks, which are frequently observed in experiments. A shock-capturing numerical algorithm is formulated to solve general problems and is used to investigate segregation in flows with weak shear
A note on vertices of simple modules
No full textWe generalize the results of [Bessenrodt 1984], showing that vertices of
simple modules of blocks of the type studied in [Eaton 2005] are
radical. This means that in order to identify simple modules whose
vertices are not radical we must consider blocks 'involving' blocks
of positive defect of non-abelian simple groups
Computing for Matrix Functions
No full textFor matrix functions
we investigate how to compute a matrix-vector product
without explicitly computing .
A general method is described that applies quadrature
to the matrix version of the Cauchy integral theorem.
Methods specific to the logarithm,
based on quadrature,
and fractional matrix powers,
based on solution of an ordinary differential equation initial value problem,
are also presente
Neighbourhoods of independence and associated geometry
No full textWe provide explicit information geometric tubular neighbourhoods containing all bivariate
processes sufficiently close to the cases of independent Poisson or Gaussian processes.
This is achieved via affine immersions of the 4-manifold of Freund bivariate distributions
and of the 5-manifold of bivariate Gaussians. We provide also the alpha-geometry for both
manifolds. The Central Limit Theorem makes our neighbourhoods of independence limiting cases
for a wide range of bivariate processes; the topological character of the results makes
them stable under small perturbations, which is important for applications
Kinematic models for non-coaxial granular materials. Part II: evaluation
No full textIn this paper we present results of numerical simulations for the evaluation of kinematic models for non-coaxial granular materials by the distinct element method (DEM). Strain-rate controlled monotonic and cyclic un-drained simple shear tests were specifically designed and evaluation criteria established for this purpose. The models examined are the double-shearing model, the double-sliding free-rotating model, and the double slip and rotation rate model (DSR2 model) proposed by the authors (see the accompanying paper). It is shown that the assumption used in the double-shearing model appears to not be in agreement with the DEM data. It is also shown that in the double-sliding free-rotating model the energy dissipation requirements appear to be unduly restrictive as a constitutive assumption. The DSR2 model, which is a hybrid of discrete micro-mechanics and continuum modelling, gives better agreement with the results of our DEM simulations, than either the double-shearing model or the double-sliding free-rotating model. Copyright © 2005 John Wiley & Sons, Ltd
Faithful functors from cancellative categories to cancellative monoids with an application to abundant semigroups
No full textWe prove that any small cancellative category admits a faithful functor to a cancellative monoid. We use our result to show that any primitive ample semigroup is a full subsemigroup of a Rees matrix semigroup where M is a cancellative monoid and P is the identity matrix. On the other hand a consequence of a recent result of Steinberg is that it is undecidable whether a finite ample semigroup embeds as a full subsemigroup of an inverse semigroup
Homoclinic Snaking near a Heteroclinic Cycle in Reversible Systems
Get PDFSnaking curves of homoclinic orbits have been found numerically in a number of ODE models from water wave theory and structural mechanics. Along such a curve infinitely many fold bifurcation of homoclinic orbits occur. Thereby the corresponding solutions spread out and develop more and more bumps (oscillations) about their own centre. A common feature of the examples is that the systems under consideration are reversible.
In this paper it is shown that such a homoclinic snaking can be caused by a heteroclinic cycle between two equilibria, one of which is a bi-focus. Using Lin’s method a snaking of 1-homoclinic orbits is proved to occur in an unfolding of such a cycle. Further dynamical consequences are discussed.
As an application a system of Boussinesq equations is considered, where numerically a homoclinic snaking curve is detected and it is shown that the homoclinic orbits accumulate along a heteroclinic cycle between a real saddle and a bi-focus equilibrium
The Russian option: Finite horizon
No full textWe show that the optimal stopping boundary for the Russian option with finite horizon can be characterized as the unique solution of a nonlinear integral equation arising from the early exercise premium representation (an explicit formula for the arbitrage-free price in terms of the optimal stopping boundary having a clear economic interpretation). The results obtained stand in a complete parallel with the best known results on the American put option with finite horizon. The key argument in the proof relies upon a local time-space formula
A Study of Segregation in Granular Gravity Driven Free Surface Flows.
Get PDFSegregation occurs in many natural and industrial free surface flows, and its study and understanding is of fundamental importance in many fields. The thesis formulates a new continuum model for this process in bi-dispersed equal density granular material. Numerous analytical solutions of this model are obtained and are shown to be in good qualitative agreement with existing experimental data. Then an accurate high order Total Variation Diminishing numerical scheme is developed to investigate time dependent flows and more complicated configurations. Additionally, the model is extended to include the effect of a passive non-viscous fluid occupying the pore space between the grains. The results of this extended model are in quantitative agreement with existing experiment data. A brief investigation of experiments to test further the predictions of this model was also undertaken. This included a study of the feed-back that segregation can have on the bulk properties of a flowing granular material, which highlights how this model could be used to investigate the important phenomenon of granular fingering in the future
Granular Vacua
Get PDFA continuum model of channelized free-surface granular flow is developed to calculate the rate at which it expands into an initially grain-free region when lateral constraints are removed. The spreading is driven by cross-stream pressure gradients and resisted by basal drag. The boundary between the granular vacuum and the flowing grains is eluciadated both in the near and far fields